


TREASURY DEPARTMENT, 

OFFICE OF THE U. S. COAST AND GEODETIC SURVEY. 

HENRY S. PRITCHETT, 

SUPERINTENDENT. 



TABLE OF FACTORS 



POE 



COMPUTING DIFFERENCES IN ELEVATION 

(IN FEET). 



TABLE OF CORRECTIONS 



FOR 



CURVATURE AND REFRACTION 

(IN FEET). 



WASHINGTON: 

GOVERNMENT PRINTING OFFICE. 
1900. 



^^ 



Vo 



a- 



.V9 



I [Extract from the United States Coast and Geodetic Survey Report, 1897-98, App. No. 8.] 

Table of factors for computiyig differences in elevation."^ 

To obtain the difference in elevation in feet multipl}' the horizontal distance in meters by the 
factor in this table corresponding to the observed angle of elevation or depression. The factors are 
given for each ten minutes, but the value for the nearest minute may be interpolated, using the column 
of differences for one minute. The result is still to be corrected where necessary for the effect of 
curvature and refraction. 

Table III. 



















Differ- 


















ence for 


Angle. 


0' 


10' 


20' 


30' 


40' 


50' 


60' 


I minute 
(fourth 
decimal 
place). 






O'OOOD 


0-0095 


0-0^191 


0-0286 


0-0382 


0-0477 


0-0573 


9-5 


I 


0-0573 


0-0668 


0-0*764 


0-0859 


0-0955 


0-1050 


0-1146 


9-6 


2 


o'ii46 


0-1241 


0-1337 


0-1432 


0-1528 


0-1624 


0-1719 


9-6 


3 


0-1719 


0-1815 


0-1911 


0-2007 


0-2I02 


0-2198 


0-2294 


9-6 


4 


0-2294 


0-2390 


0-2486 


0-2582 


0-2678 


0-2774 


0*2870 


9-6 


5 


0-2870 


0-2967 


0-3063 


0-3159 


0-3255 


0-3352 


0-3448 


9-6 


6 


0-3448 


0-3545 


0-3641 


0-3738 


0-3835 


0-3932 


p-4028 


9-7 


, 7 


0-4028 


0-4125 


0-4222 


0-4319 


0-4416 


0-4514 


0-4611 


9-7 


8 


0-4611 


0-4708 


0-4S06 


0-4903 


0-5001 


0-5098 


0-5196 


9-8 


9 


0-5196 


0-5294 


0-5392 


0-5490 


0-5588 


0-5687 


0-5785 


9-8 


10 


, 0-5785 


0-5884 


0-5982 


0-60S1 


0-6179 


0-6278 


0-6377 


9-9 


II 


0-6377 


0-6476 


0-6576 


0-6675 


0-6774 


0-6874 


0-6974 


9-9 


12 


0-6974 


0-7073 


0-7173 


0-7273 


0-7374 


0-7474 


0-7574 


lo-o 


13 


0-7574 


0-7675 


0-7776 


0-7877 


0-7978 


0-8079 


o-8i8o 


lo-i 


14 


o-8i8o 


0-S282 


0-8383 


0-8485 


0-8587 


0-8689 


0-8791 


10-2 


15 


0-8791 


0-8893 


0-8996 


0-9099 


0-9201 


0-9304 


0-9408 


10-3 


16 


0-9408 


0-9511 


0-9615 


0-97x8 


0-9822 


0-9926 


I -003 1 


10-4 


17 


1-0031 


I '0135 


I -0240 


1-0344 


I -0449 


1 -0555 


I -0660 


10-5 


18 


I -0660 


I -0766 


1-0872 


I -0978 


I-I0S4 


1-1190 


1-1297 


10-6 


19 


1-1297 


I -1404 


1-1511 


1-1618 


I-I726 


1-1833 


1-1941 


IO-7 


20 


1-1941 


I 2050 


1-2158 


1-2266 


1-2375 


1-2485 


1-2594 


10-9 


21 


1-2594 


1-2704 


1-2813 


1-2924 


1 -3034 


1-3144 


1-3255 


ii-o 


22 


1-3255 


1-3367 


1-3478 


1-3590 


1-3702 


1-3814 


1-3926 


11-2 


23 


1-3926 


1-4039 


1-4152 


1-4266 


1-4379 


1-4493 


1-4607 


11-4 


24 


I -4607 


1-4722 


1-4836 


1-4952 


1-5067 


1-5183 


1-5299 


11-5 


25 


1-5299 


i'54i5 


1-5532 


I -5649 


1-5766 


1-5884 


I -6002 


11-7 


26 


I -6002 


I -61 20 


1-6239 


1-6358 


1-6477 


1-6597 


1-6717 


11-9 


27 


1-6717 


1-6837 


1-6958 


1-7079 


1-7200 


1-7322 


1-7444 


12-1 


28 


1-7444 


1-7567 


1-7690 


1-7814 


1-7937 


I -8061 


1-8186 


12-4 


29 


1-8186 


1-8311 


1-8436 


1-8562 


1-8688 


1-8815 


I "8942 


12-6 


30 


I -8942 


1-9069 


1-9197 


1-9326 


1-9454 


1-9584 


1-9713 


12-9 


31 


1-9713 


1-9843 


1 -9974 


2-0105 


2-0236 


2-0368 


2-0501 


13-1 


32 


2-0501 


2-0634 


2-0767 


2-0901 


2-1036 


2-1171 


2-1306 


13-4 


33 


2-1306 


2-1442 


2-1578 


2-1715 


2-1853 


2-1991 


2-2130 


13-7 


34 


2-2130 


22269 


2-2408 


2-2548 


2-2689 


2-2831 


2-2973 


14-0 


35 


2-2973 


2-3115 


2-3258 


2-3402 


2-3546 


2-3691 


2-3837 


14-4 


36 


2-3837 


2-3983 


2-4130 


2-4277 


2-4425 


2-4574 


2-4723 


14-8 


37 


2-4723 


2-4873 


2-5023 


2-5175 


2-5327 


2-5479 


2-5633 


15-2 


38 


2-5633 


2-5787 


2-5942 


2-6097 


2-6253 


2-6410 


2-6568 


15-6 


39 


2-6568 


2-6726 


2-6885 


2-7045 


2-7206 


2-7367 


2-7530 


i6-o 


40 


2-7530 


2-7692 


2-7856 


2 -802 1 


2-8i86 


2-8353 


2-8520 


i6-5 


41 


2-8520 


2-8688 


2-8857 


2-9026 


2-9197 


2-9368 


2-9541 


17-0 


42 


2-9541 


2-9714 


2-9888 


3-0063 


3-0239 


3-0416 


3-0594 


17-6 


43 


3 '0594 


3-0773 


3-0953 


3-1134 


3-1316 


3-1499 


3-1683 


18-1 


44 


3-1683 


3-1868 


3-2054 


3-2241 


3-2429 


3-2618 


3-2808 


i8-8 



* Furnished by G. R. Putnam, Assistant, Coast and Geodetic Survey. 




:^d?^ 






[Extract from the United States Coast and Geodetic Survey Report, 1897-98, App. No. 8.] 
Table of corrections for airvatiirc and refraction/^ 

The correction in feet for the combined effect of curvature and refraction is given for each 100 
meters' distance, the thousands of meters being given in the column to the left and the hundreds in 
the upper line. The correction is to be added to the dijference of elevation for angles of elevation 
and subtracted for angles of depression, or it is always to be added to the uncorrected elevation of the 
point to be deteririined from point of observation. 

Example: At a station whose elevation is i 000 feet (at telescope), angle to signal ^3^ elevation, 
horizontal distance = 5 000 meters. From Table III factor is o"i7i9, which multiplied by 5 000 = 859"5 
feet. From Table IV correction is 5 "5 feet. Corrected difference of elevation ^ Ssg'S + 55 ^865 
feet, which added to i 000 = i 865 feet for elevation of signal. If the above angle to signal be 3° 
depression, then corrected difference of elevation = 859"5 — 5"5 ^= 854'o feet, which makes height of 
signal = I 000 — 854 "o ^= i46'o feet. 

Table IV. 



Distance in 
meters. 





100 


200 


300 


400 


500 


600 
Feet. 


700 


800 


900 


I 000 




Feel. 


Feet. 


Feet. 


Feet. 


Feet. 


Feet. 


Feet. 


Feet. 


heet. 


Feet. 





O'O 


Q-O 


O-Q 


Q-Q 


O-Q 


O'l 


Q-l 


o-i 


o-i 


O-I 


0'2 


I 000 


0-2 


0-3 


0-3 


0-4 


0-4 


0-5 


0-6 


0-6 


07 


0-8 


0-9 


2 000 


0-9 


I.O 


I'l 


1-2 


I '3 


I "4 


I '5 


1-6 


17 


1-9 


2-0 


3 coo 


2'0 


2-1 


2-3 


2-4 


2-6 


27 


2-9 


3'o 


3"2 


3'4 


3-5 


4 000 


3-5 


37 


3-9 


4'i 


4-3 


4-5 


47 


4-9 


5-1 


5'3 


5-5 


5 000 


5-5 


5-8 


6-0 


6-2 


6-5 


67 


7-0 


7-2 


7-4 


77 


8-0 


6 000 


8-0 


8-2 


8-5 


8-8 


9-1 


9'4 


97 


lO'O 


IO-2 


IO-6 


10-9 


7 000 


io'9 


II-2 


II-5 


II-8 


I2-I 


12-5 


12-8 


i3"i 


13-5 


13-8 


14-2 


8 000 


14-2 


14-5 


14-9 


15-3 


15-6 


i6-o 


16-4 


i6-8 


17-2 


17-6 


i8-o 


9 000 


i8-o 


18-4 


i8-8 


19-2 


I9'6 


20 'O 


20-4 


20 -8 


21-3 


217 


22-2 


10 000 


22-2 


22-6 


23 'o 


23-5 


24-0 


24-4 


24-9 


25'4 


25-8 


26-3 


26-8 


II 000 


26-8 


27-3 


27-8 


28-3 


28-8 


29'3 


29-8 


30-3 


30-8 


3i'4 


31-9 


12 000 


31-9 


32-4 


33 'o 


33-5 


34-1 


34-6 


35-2 


357 


36-3 


36-9 


37-4 


13 OQO 


37'4 


38-0 


38-6 


39-2 


39-8 


40-4 


41 "O 


41-6 


42-2 


42-8 


43-4 


14 000 


43-4 


44' I 


447 


45-3 


46-0 


46-6 


47-2 


47'9 


48-5 


49-2 


49-8 


15 000 


49-8 


50-5 


51-2 


51-9 


52-5 


53'2 


53'9 


54'6 


55 '3 


56'o 


567 


16 000 


567 


57-4 


58-2 


58-9 


59'6 


60-3 


61 -o 


6i-8 


62-5 


63-3 


64-0 


17 000 


64-0 


64-8 


65-6 


66-3 


67-1 


67-9 


68-6 


69-4 


70-2 


71-0 


71-8 


18 000 


71-8 


72-6 


73-4 


74-2 


75-0 


75-8 


767 


77-5 


78-3 


79-1 


80 -o 


19 000 


80 -0 


8o-8 


817 


82-5 


83-4 


84-2 


85-1 


86 -o 


86-9 


877 


88-6 



* Furnished by G. R. Putnam, Assistant, Coast and Geodetic Survey. 



LIBRARY OF CONGRESS 



021 607 659 fl 



